Surface Area of Intersection with Skull
First cut the part of the skull that is sticking through the plane using the bisect tool:
Then delete the rest of the faces so you're left with only the part you need to measure:
Join up all the edges to get a plane, and then delete everything else so only the plane you made is left.
Lastly go to user preferences and activate the 3d printing addon (found under mesh) and it will tell you the area of your plane. I would add more screenshots, but i can only post 2 since i dont have enough reputation.